Have we underestimated the power of image undistortion?

An indispensable pre-processing step for image-based 3D reconstruction or photogrammetry tasks is undistortion, which is employed for correcting the non-linear projection of the surface points of objects onto the image plane due to lens distortion. To deal with this undesirable artifact, state-of-the-art methods focus on directly recovering the 2D coordinates of image points from distorted images, where a mapping function rather than the real undistortion model is obtained. Contrary to the standard undistortion, we explicitly consider the imaging process of a finite projective camera: the projection of a 3D point onto the image plane is determined not only by the lens, but also by the intrinsic parameters of the camera. After an appropriate transformation of the intrinsic matrix for parameter reduction, it is shown that an exact recovery of the real undistorted coordinates can be achieved for most of the commonly used undistortion functions. Interestingly, a simultaneous estimation of the two intrinsic parameters, aspect ratio a and skew factor s, is also embedded in the undistortion process, which demonstrates the underestimated power of image undistortion in a conventional way. As a benefit of considering the physical model instead of fitting a mapping function, improved undistortion performance can be achieved.